The height of the cone is 4. The generatrix is inclined to the base plane at an angle of 30 degrees. find the generatrix of the cone.

Let’s make an axial section of the cone. It is an isosceles triangle ABC:
Here VO = h = 4 is the height of the cone;
BC – generatrix of the cone;
<BOC = 90 °;
<BCO = 30 °.
Consider a BOC right-angled triangle. By definition of sine:
sin (BCO) = BO / BC;
BC = BO / sin (BCO) = 4 / sin 30 ° = 4 / 0.5 = 8.
Answer: the generator of the cone is 8.